Pareto optimality, or pareto efficiency, is a powerful economic concept used to eliminate inefficient decisions. The term is named after Vilfredo Pareto, italian economist.

In general, decision $f$ is pareto superior to $f'$ if and only if:
\begin{equation}
\forall_{i\in N}\,u_i(f)>=u_i(f')
\end{equation}
where $u_i$ is the $i$-th criterion and at least one inequality is sharp.

Decision $f$ is pareto-optimal if there is no decision $f'$ pareto superior to $f$. Set of all pareto-optimal decisions is called pareto-optimal set. 

%The basic idea is that one usually cannot directly compare two allocations of goods or income. For instance having two decision criteria, one allocation is prefered taking into account first criterion whilst other allocation is preferred taking into account the latter. In this situation two possibilities are indifferent in the sense of Pareto. 

%ver1 Otherwise, if one allocation is prefered or indifferent to the other allocation considering every criterion, provided at least in one case preference is strict, it is called Pareto superior.

%ver2 Among two allocations, one is called Pareto superior to the other if, and only if it is 
%ver2.1 strictly prefered in at least one criterion and 
%ver2.2 prefered or indifferent to the other allocation considering every criterion, provided at least in one case preference is strict.


